If we explicitly apply the cubic polynomial svm to the original $784-$dimensional raw pixel features, the resulting representation would be of massive dimensionality. Instead, we will apply the cubic polynomial svm to the $10-$dimensional PCA representation of our training data which we will have to calculate just as we calculated the $18-$dimensional representation in the previous problem. Use the sklearn package and build the SVM model on your local machine. Use random$\_$state $=0,$ kernel $=$ 'poly', degree $=3,$ and default values for other parameters.

If you have done everything correctly, cubic polynomial svm should perform better $($on the test set$)$ using these features than either the $18-$dimensional principal components or raw pixels. The error on the test set using the cubic polynomial svm should only be around $0\mathrm{.}06,$ demonstrating the power of nonlinear classification models.

Error rate for $10-$dimensional PCA features using cubic polynomial svm $=$